Introduction to the Anderson-Darling Test (short) - Engineering Statistics
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TLDRThe Anderson-Darling goodness of fit test is a hypothesis test used to assess whether a dataset follows a specified distribution. Unlike some tests, it is not limited to assessing normal distribution and can be applied to various distributions. The test works by calculating a weighted comparison of each measurement's probability against expected values, with an emphasis on the tails of the distribution. This approach makes it more sensitive to deviations, particularly in the tails. The process involves determining a test statistic, which is then used to compute a P-value through piecewise functions. Comparing this P-value against a critical value helps in deciding if the data adheres to the specified distribution.
Takeaways
- 📊 The Anderson-Darling test checks if data follows a specified distribution.
- ❗ It's not limited to the normal distribution.
- 🔍 It gives more weight to the tails of the distribution.
- 📈 Uses weighted z-scores to compare expected and actual values.
- ⚙️ Tail weight sensitivity makes it more selective.
- 🔣 Calculates P-value using test statistics and piecewise functions.
- 💡 Helps decide if data aligns with a given distribution.
- 🔬 Frequently used in engineering.
- 📉 More emphasis on tail discrepancies than other tests.
- 💼 Useful for multiple distributions.
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The Anderson-Darling test is a versatile goodness-of-fit test used in engineering to assess whether data follows a specified distribution, not limited to just the normal distribution. The test involves a hypothesis: the null hypothesis claims that the data conforms to the specified distribution, while the alternative suggests otherwise. The test calculates a weighted comparison of z-scores, emphasizing discrepancies, particularly in the tails of the distribution. This trait renders the Anderson-Darling test particularly sensitive, often making it the first choice for normality testing. The process involves summing weighted values and scaling them by the sample size to get the test statistic, which is then used to derive a p-value through piecewise functions. Comparing the p-value to a critical threshold helps determine if the data fits the specified distribution.
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What does the Anderson-Darling test assess?
The Anderson-Darling test assesses whether data follows a specified distribution, not limited to normal distribution.
What is the null hypothesis in the Anderson-Darling test?
The null hypothesis is that the data follows the specified distribution.
What types of distributions can the Anderson-Darling test be used for?
The Anderson-Darling test can be used for multiple distributions, not just the normal distribution.
How does the Anderson-Darling test work?
It calculates a weighted comparison of the probability of each measurement's z-score to determine discrepancies between actual measurements and expected values from the distribution.
Why is the Anderson-Darling test considered selective?
Because it puts a higher weight on the tails of the distribution, making it more sensitive to deviations in heavy tails.
What does the test statistic represent in the Anderson-Darling test?
The test statistic represents a scaled sum of weighted values derived from comparing sample z-scores to expected z-scores.
How is the P-value calculated in the Anderson-Darling test?
The P-value is calculated using a set of piecewise functions based on the Anderson-Darling test statistic.
What is the significance of comparing the P-value with a critical value?
It helps determine whether the data follows the specified distribution or not based on whether the P-value is less than the critical value.
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- Anderson-Darling test
- goodness of fit
- hypothesis testing
- distribution
- z-score
- test statistic
- P-value
- critical value
- heavier tails
- engineering